We discussed your Mixed-up Socks question in our Math club hour and
we found the answer using coloured pens. We made a combination
using three socks. When we made pairs with red and blue socks, the
other green and red socks, so the third pair must be green and
blue. We found only one way:

Lucy from Bishop Ramsey School, Priya from
Loughborough High School and Katarina all then went on to introduce
another pair of socks of a different colour. They each foundtwo
ways to mix up the socks this time. However, Bafiar, Yunus and
Alper found more:

For four pairs of socks we found three ways. For example if the
fourth pair is purple:
1. Green-Blue, Green-Purple, Red-Purple, Red-Blue
2. Red-Green, Green-Purple, Purple-Blue, Red-Blue
3. Green-Blue, Red-Purple, Purple-Blue, Red-Green

I wonder if you can explain how we know we
have got all the different ways?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.